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Although the recursive logit (RL) model has been recently popular and has led to many applications and extensions, an important numerical issue with respect to the computation of value functions remains unsolved. This issue is particularly significant for model estimation, during which the parameters are updated every iteration and may violate the feasibility condition of the value function. To solve this numerical issue of the value function in the model estimation, this study performs an extensive analysis of a prism-constrained RL (Prism-RL) model proposed by Oyama and Hato (2019), which has a path set constrained by the prism defined based upon a state-extended network representation. The numerical experiments have shown two important properties of the Prism-RL model for parameter estimation. First, the prism-based approach enables estimation regardless of the initial and true parameter values, even in cases where the original RL model cannot be estimated due to the numerical problem. We also successfully captured a positive effect of the presence of street green on pedestrian route choice in a real application. Second, the Prism-RL model achieved better fit and prediction performance than the RL model, by implicitly restricting paths with large detour or many loops. Defining the prism-based path set in a data-oriented manner, we demonstrated the possibility of the Prism-RL model describing more realistic route choice behavior. The capture of positive network attributes while retaining the diversity of path alternatives is important in many applications such as pedestrian route choice and sequential destination choice behavior, and thus the prism-based approach significantly extends the practical applicability of the RL model.